-
-
-let rewrite_tac ~term:equality (proof,goal) =
- let module C = Cic in
- let module U = UriManager in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,gty = CicUtil.lookup_meta goal metasenv in
- let eq_ind_r,ty,t1,t2 =
- match CicTypeChecker.type_of_aux' metasenv context equality with
- C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
- when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
- let eq_ind_r =
- C.Const
- (HelmLibraryObjects.Logic.eq_ind_r_URI,[])
- in
- eq_ind_r,ty,t1,t2
- | _ ->
- raise
- (ProofEngineTypes.Fail
- "Rewrite: the argument is not a proof of an equality")
- in
- let pred =
- let gty' = CicSubstitution.lift 1 gty in
- let t1' = CicSubstitution.lift 1 t1 in
- let gty'' =
- ProofEngineReduction.replace_lifting
- ~equality:ProofEngineReduction.alpha_equivalence
- ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
- in
- C.Lambda
- (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
- ty, gty'')
- in
- let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
- let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
- let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
-
- let (proof',goals) =
- PrimitiveTactics.exact_tac
- ~term:(C.Appl
- [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
- ((curi,metasenv',pbo,pty),goal)
- in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
-;;
-
-
-let rewrite_simpl_tac ~term status =
- Tacticals.then_
- ~start:(rewrite_tac ~term)
- ~continuation:
- (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
- status
-;;
-
-
-let rewrite_back_tac ~term:equality (proof,goal) =
- let module C = Cic in
- let module U = UriManager in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,gty = CicUtil.lookup_meta goal metasenv in
- let eq_ind_r,ty,t1,t2 =
- match CicTypeChecker.type_of_aux' metasenv context equality with
- C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
- when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
- let eq_ind_r =
- C.Const (HelmLibraryObjects.Logic.eq_ind_URI,[])
- in
- eq_ind_r,ty,t2,t1
- | _ ->
- raise
- (ProofEngineTypes.Fail
- "Rewrite: the argument is not a proof of an equality")
- in
- let pred =
- let gty' = CicSubstitution.lift 1 gty in
- let t1' = CicSubstitution.lift 1 t1 in
- let gty'' =
- ProofEngineReduction.replace_lifting
- ~equality:ProofEngineReduction.alpha_equivalence
- ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
- in
- C.Lambda
- (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
- ty, gty'')
- in
- let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context in
- let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
-
- let (proof',goals) =
- PrimitiveTactics.exact_tac
- ~term:(C.Appl
- [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
- ((curi,metasenv',pbo,pty),goal)
- in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
-
-;;
-
-
-let rewrite_back_simpl_tac ~term status =
- Tacticals.then_
- ~start:(rewrite_back_tac ~term)
- ~continuation:
- (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
- status
+
+let rec rewrite_tac ~direction ~pattern equality =
+ let _rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
+ =
+ let module C = Cic in
+ let module U = UriManager in
+ let module PET = ProofEngineTypes in
+ let module PER = ProofEngineReduction in
+ let module PEH = ProofEngineHelpers in
+ let module PT = PrimitiveTactics in
+ assert (wanted = None); (* this should be checked syntactically *)
+ let proof,goal = status in
+ let curi, metasenv, pbo, pty = proof in
+ let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
+ match hyps_pat with
+ he::(_::_ as tl) ->
+ PET.apply_tactic
+ (Tacticals.then_
+ (rewrite_tac ~direction
+ ~pattern:(None,[he],Cic.Implicit None) equality)
+ (rewrite_tac ~direction ~pattern:(None,tl,concl_pat) equality)
+ ) status
+ | [_] as hyps_pat when concl_pat <> Cic.Implicit None ->
+ PET.apply_tactic
+ (Tacticals.then_
+ (rewrite_tac ~direction
+ ~pattern:(None,hyps_pat,Cic.Implicit None) equality)
+ (rewrite_tac ~direction ~pattern:(None,[],concl_pat) equality)
+ ) status
+ | _ ->
+ let arg,dir2,tac,concl_pat,gty =
+ match hyps_pat with
+ [] -> None,true,(fun ~term _ -> PT.exact_tac term),concl_pat,gty
+ | [name,pat] ->
+ let rec find_hyp n =
+ function
+ [] -> assert false
+ | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
+ Cic.Rel n, CicSubstitution.lift n ty
+ | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet! But does this make any sense?*)
+ | _::tl -> find_hyp (n+1) tl
+ in
+ let arg,gty = find_hyp 1 context in
+ let last_hyp_name_of_status (proof,goal) =
+ let curi, metasenv, pbo, pty = proof in
+ let metano,context,gty = CicUtil.lookup_meta goal metasenv in
+ match context with
+ (Some (Cic.Name s,_))::_ -> s
+ | _ -> assert false
+ in
+ let dummy = "dummy" in
+ Some arg,false,
+ (fun ~term typ ->
+ Tacticals.seq
+ ~tactics:
+ [ProofEngineStructuralRules.rename name dummy;
+ PT.letin_tac
+ ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
+ ProofEngineStructuralRules.clearbody name;
+ ReductionTactics.change_tac
+ ~pattern:
+ (None,[name,Cic.Implicit (Some `Hole)],Cic.Implicit None)
+ (ProofEngineTypes.const_lazy_term typ);
+ ProofEngineStructuralRules.clear dummy
+ ]),
+ pat,gty
+ | _::_ -> assert false
+ in
+ let if_right_to_left do_not_change a b =
+ match direction with
+ | `RightToLeft -> if do_not_change then a else b
+ | `LeftToRight -> if do_not_change then b else a
+ in
+ let ty_eq,ugraph =
+ CicTypeChecker.type_of_aux' metasenv context equality
+ CicUniv.empty_ugraph in
+ let (ty_eq,metasenv',arguments,fresh_meta) =
+ ProofEngineHelpers.saturate_term
+ (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
+ let equality =
+ if List.length arguments = 0 then
+ equality
+ else
+ C.Appl (equality :: arguments) in
+ (* t1x is t2 if we are rewriting in an hypothesis *)
+ let eq_ind, ty, t1, t2, t1x =
+ match ty_eq with
+ | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
+ when LibraryObjects.is_eq_URI uri ->
+ let ind_uri =
+ if_right_to_left dir2
+ LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
+ in
+ let eq_ind = C.Const (ind_uri uri,[]) in
+ if dir2 then
+ if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
+ else
+ if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
+ | _ -> raise (PET.Fail (lazy "Rewrite: argument is not a proof of an equality")) in
+ (* now we always do as if direction was `LeftToRight *)
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ ~subst:[] metasenv' context C.Anonymous ~typ:ty in
+ let lifted_t1 = CicSubstitution.lift 1 t1x in
+ let lifted_gty = CicSubstitution.lift 1 gty in
+ let lifted_conjecture =
+ metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
+ let lifted_pattern =
+ Some (fun _ m u -> lifted_t1, m, u),[],CicSubstitution.lift 1 concl_pat
+ in
+ let subst,metasenv',ugraph,_,selected_terms_with_context =
+ ProofEngineHelpers.select
+ ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
+ ~pattern:lifted_pattern in
+ let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
+ let what,with_what =
+ (* Note: Rel 1 does not live in the context context_of_t *)
+ (* The replace_lifting_csc 0 function will take care of lifting it *)
+ (* to context_of_t *)
+ List.fold_right
+ (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
+ selected_terms_with_context ([],[]) in
+ let t1 = CicMetaSubst.apply_subst subst t1 in
+ let t2 = CicMetaSubst.apply_subst subst t2 in
+ let equality = CicMetaSubst.apply_subst subst equality in
+ let abstr_gty =
+ ProofEngineReduction.replace_lifting_csc 0
+ ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
+ let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
+ let pred = C.Lambda (fresh_name, ty, abstr_gty) in
+ (* The argument is either a meta if we are rewriting in the conclusion
+ or the hypothesis if we are rewriting in an hypothesis *)
+ let metasenv',arg,newtyp =
+ match arg with
+ None ->
+ let gty' = CicSubstitution.subst t2 abstr_gty in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,gty')::metasenv' in
+ metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *)
+ | Some arg ->
+ let gty' = CicSubstitution.subst t1 abstr_gty in
+ metasenv,arg,gty'
+ in
+ let exact_proof =
+ C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
+ in
+ let (proof',goals) =
+ PET.apply_tactic
+ (tac ~term:exact_proof newtyp) ((curi,metasenv',pbo,pty),goal)
+ in
+ let goals =
+ goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
+ ~newmetasenv:metasenv')
+ in
+ (proof',goals)
+ in
+ ProofEngineTypes.mk_tactic (_rewrite_tac ~direction ~pattern equality)
+
+
+let rewrite_simpl_tac ~direction ~pattern equality =
+ let rewrite_simpl_tac ~direction ~pattern equality status =
+ ProofEngineTypes.apply_tactic
+ (Tacticals.then_
+ ~start:(rewrite_tac ~direction ~pattern equality)
+ ~continuation:
+ (ReductionTactics.simpl_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)))
+ status
+ in
+ ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)